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MAT 566: Differential Topology

Course Instructor: Mark McLean

Monday, Wednesday 2:30pm-3:50pm in Physics P122.

This will be a course mainly on characteristic classes, which are particular invariants of vector bundles. These will include Stiefel Whitney classes, Chern classes and Pontrjagin classes. We will also cover classifying spaces and in particular Grassmannians, and the Hirzebruch signature theorem. At the end of the course we will combine many of these ideas to construct a smooth 7 manifold which is homeomorphic but not diffeomorphic to the 7 dimensional sphere. We will be following the book Characteristic Classes, Annals of Mathematics Studies 76, by John Milnor and James Stasheff.

Office Hours: Tuesday, Thursday 11am-12pm (Math 4-101B).

Lecture Notes:
Part 1
Part 2
Part 3
Part 4
Part 5
Part 6
Part 7
Part 8
Part 9
Part 10
Part 12
Part 13
Part 14
Part 15
Part 16
Part 17
Part 18


Exercises
Exercise Sheet (not compulsory)

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